Best uniform approximation of semi-Lipschitz function by extension

Abstract

In this paper we consider the problem of best uniform approximation of a real valued semi-Lipschitz function \(F\) defined on an asymmetric metric space \((X,d)\), by the elements of the set \(E_{d}(F|_{Y})\) of all extensions of \(F|_{Y}(Y\subset X)\), preserving the smallest semi-Lipschitz constant. It is proved that, this problem has always at least a solution, if \((X,d)\) is \((d,\overline{d})\)-sequentially compact, or of finite diameter.

Authors

Costică Mustăţa
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academi,  Romania

Keywords

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Paper coordinates

C. Mustăţa, Best uniform approximation of semi-Lipschitz function by extension, Rev. Anal. Numér. Théor. Approx. 36 (2007) 2, pp. 161-171.

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About this paper

Journal

Revue d’Analyse Numer. Theor. Approx.

Publisher Name

Publishing House of the Romanian Academy

Print ISSN

2501-059X

Online ISSN

2457-6794

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